Claudia Negulescu

An accelerated algorithm for 2D simulations of the quantum ballistic transport in nanoscale MOSFETs

An accelerated algorithm for the resolution of the coupled Schrodinger/Poisson system, with open boundary conditions, is presented. This method improves the sub-band decomposition method (SDM) introduced in [N. Ben Abdallah, E. Polizzi, Subband decomposition approach for the simulation of quantum electron transport in nanostructures, J. Comput. Phys. 202 (1) (2005) 150-180]. The principal feature of the here presented model consists in an inexpensive and fast resolution of the Schrodinger equation in the transport direction, due to the application of WKB techniques. Oscillating WKB basis elements are constructed and replace the piecewise polynomial interpolation functions used in SDM. This procedure is shown to reduce considerably the computational time, while keeping a good accuracy.

WKB-Based Schemes for the Oscillatory 1D Schrödinger Equation in the Semiclassical Limit

An efficient and accurate numerical method is presented for the solution of highly oscillatory differential equations. While standard methods would require a very fine grid to resolve the oscillations, the presented approach uses first an analytic (second order) WKB-type transformation, which filters out the dominant oscillations. The resulting ODE is much smoother and can hence be discretized on a much coarser grid, with significantly reduced numerical costs. In many practically relevant examples, the method is even asymptotically correct w.r.t. the small parameter

Numerical analysis of a multiscale finite element scheme for the resolution of the stationary Schrödinger equation

\varepsilon

Closure of the Strongly Magnetized Electron Fluid Equations in the Adiabatic Regime

that identifies the oscillation wavelength. Indeed, in these cases, the error then vanishes for

Hybrid Classical-Quantum Models for Charge Transport in Graphene with Sharp Potentials

\varepsilon\to0

A ONE DIMENSIONAL QUANTUM TRANSPORT MODEL WITH SMALL COHERENCE LENGTHS

, even on a fixed spatial mesh. Applications to the stationary Schrodinger equation are presented.

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

A numerical method for the resolution of the one-dimensional Schrödinger equation with open boundary conditions was presented in N. Ben Abdallah and O. Pinaud (Multiscale simulation of transport in an open quantum system: resonances and WKB interpolation. J. Comp. Phys. 213(1), 288–310 (2006)). The main attribute of this method is a significant reduction of the computational cost for a desired accuracy. It is based particularly on the derivation of WKB basis functions, better suited for the approximation of highly oscillating wave functions than the standard polynomial interpolation functions. The present paper is concerned with the numerical analysis of this method. Consistency and stability results are presented. An error estimate in terms of the mesh size and independent on the wavelength λ is established. This property illustrates the importance of this method, as multiwavelength grids can be chosen to get accurate results, reducing by this manner the simulation time.

Asymptotic Transition from Kinetic to Adiabatic Electrons along Magnetic Field Lines

We derive closure relations for a plasma fluid model, issued from the BGK equation for electrons in a strong magnetic field. Our scaling of the BGK equation leads in the asymptotic limit

Diffusion limit of a generalized matrix Boltzmann equation for spin-polarized transport

\varepsilon \to 0

Adiabatic quantum-fluid transport models

towards the adiabatic electron regime, where